Differential amplifiers are circuits used to amplify a difference between two input voltages of the amplifier. An example of a differential amplifier is an operational amplifier (“op-amp”) which receives a non-inverting input (V+) and an inverting input (V−) and outputs a single-ended output (Vout). Feedback between the output and the inverting input may be used to control a gain of the circuit.
An instrumentation amplifier may be a circuit which uses a main amplifier to amplify a differential signal and one or more additional amplifiers as input buffers. Instrumentation amplifiers may be used to test electronic equipment. In one example application, instrumentation amplifiers may be used to measure a resistance of connections (e.g., through silicon/substrate vias, TSVs) between semiconductor dies or chips of a semiconductor memory device.
FIG. 1 is a schematic diagram of a prior art instrumentation amplifier. The instrumentation amplifier 100 includes a first amplifier 102 coupled to a second amplifier 104. The first amplifier 102 includes two operational amplifiers OP1 and OP2. The outputs of OP1 and OP2 are coupled by resistors R21, R1, and R22 which are coupled in series from the output of OP1 to the output of OP2. The inverting input of OP1 is coupled between resistors R21 and R1, and the inverting input of OP2 is coupled between R1 and R22. The non-inverting input of OP1 is coupled to an input voltage INp, while the non-inverting input of OP2 is coupled to an input voltage INn. The outputs of OP1 serves as in input IA1p to the second amplifier 104, and the output of OP2 serves as an input IA1n to the second amplifier 104. The operational amplifiers OP1 and OP2 may act as input buffers on the inputs INp and INn respectively.
The second amplifier 104 includes an op-amp OP3. The input IA1p is coupled to ground via resistors R31 and variable resistor R41 coupled in series. The non-inverting input of OP3 is coupled between R31 and R41. The input IA1n is coupled to the output of OP3 via resistors R32 and R42, which are coupled in series. The inverting input of OP3 is coupled between R32 and R42. The resistors R21 and R22 are equal in resistance to each other. The resistors R31 and R32 are equal in resistance, and the variable resistor R41 has a default resistance equal the resistance R42.
The first amplifier 102 receives the voltages INp and INn as inputs, and provides voltages IA1p and IA1n as outputs. The input voltages may be expressed as a common voltage Vcom (a voltage equal across the differential inputs) and a differential signal amplitude Vin. Thus, the input voltage INp may be expressed as Vcom+(½)*Vin, while the voltage at Inn may be expressed as Vcom−(½)*Vin. From this, the output voltages V(1A1p) and V(1A1n) may be calculated by equations 1 and 2 below:
                              V          ⁡                      (                          IA              ⁢                                                          ⁢              1              ⁢              p                        )                          =                              V            ⁢                                                  ⁢            com                    +                      Vin            ⁡                          (                                                1                  2                                +                                                      R                    ⁢                                                                                  ⁢                    2                                                        R                    ⁢                                                                                  ⁢                    1                                                              )                                +                      VOS            ⁢                                                  ⁢            1            ⁢                          (                              1                +                                                      R                    ⁢                                                                                  ⁢                    2                                                        R                    ⁢                                                                                  ⁢                    1                                                              )                                -                      VOS            ⁢                                                  ⁢            2            ⁢                          (                                                R                  ⁢                                                                          ⁢                  2                                                  R                  ⁢                                                                          ⁢                  1                                            )                                                          Eqn        .                                  ⁢        1                                          V          ⁡                      (                          IA              ⁢                                                          ⁢              1              ⁢              n                        )                          =                  Vcom          -                      Vin            ⁡                          (                                                1                  2                                +                                                      R                    ⁢                                                                                  ⁢                    2                                                        R                    ⁢                                                                                  ⁢                    1                                                              )                                -                      VOS            ⁢                                                  ⁢            1            ⁢                          (                                                R                  ⁢                                                                          ⁢                  2                                                  R                  ⁢                                                                          ⁢                  1                                            )                                +                      VOS            ⁢                                                  ⁢            2            ⁢                          (                              1                +                                                      R                    ⁢                                                                                  ⁢                    2                                                        R                    ⁢                                                                                  ⁢                    1                                                              )                                                          Eqn        .                                  ⁢        2            
R2 is the value of the resistors R21 and R22, which have an equal resistance to each other. VOS1 and VOS2 are offset voltages which may exist on the input voltages INp and INn of the non-inverting inputs of the op-amps OP1 and OP2, respectively. The voltages VOS1 and VOS2, as shown in FIG. 1, may have a reversed polarity to each other. The difference Vdif between the two outputs V(1A1p) and V(1A1n) may be derived by subtracting Eqn. 2 from Eqn. 1 to yield equation 3 below:
                    Vdif        =                              (                          1              +                              2                ⁢                                                      R                    ⁢                                                                                  ⁢                    2                                                        R                    ⁢                                                                                  ⁢                    1                                                                        )                    ⁢                      (                          Vin              +                              VOS                ⁢                                                                  ⁢                1                            -                              VOS                ⁢                                                                  ⁢                2                                      )                                              Eqn        .                                  ⁢        3            
From the above equations, the amplification factor (gain) Acom1 of the common voltage Vcom and the amplification factor A1 of the differential signal Vin may be determined by equations 4 and 5 below:Acom1=1  Eqn. 4
                              A          ⁢                                          ⁢          1                =                  1          +                      2            ⁢                                          R                ⁢                                                                  ⁢                2                                            R                ⁢                                                                  ⁢                1                                                                        Eqn        .                                  ⁢        5            
Accordingly, since the common gain Acom1 is unity, the common voltage between the differential inputs INp and INn will not be increased, while the differential voltage Vin will increase by a factor based on the value of R2 and R1. The second amplifier 104 receives the amplified outputs provided by the first amplifier 102 as an input. The common input voltage between inputs IA1p and IA1n remains Vcom, since the Acom1 of the first amplifier 102 is 1. If the difference between the offset voltages VOS1 and VOS2 is assumed to be negligible (e.g., VOS1=VOS2), then the voltage of IA1p is Vcom+(½)*Vdif, while the voltage of IA1n is Vcom−(½)*Vdif. Thus, the voltage Vout provided by the second amplifier 104 may be estimated by equation 6 below:
                    VOUT        ≈                              Vdif            ⁡                          (                                                R                  ⁢                                                                          ⁢                  4                                                  R                  ⁢                                                                          ⁢                  3                                            )                                +                      VOS            ⁢                                                  ⁢            3            ⁢                          (                              1                +                                                      R                    ⁢                                                                                  ⁢                    4                                                        R                    ⁢                                                                                  ⁢                    3                                                              )                                +                      Vcom            ⁡                          (                                                                    R                    ⁢                                                                                  ⁢                    4                                                                              R                      ⁢                                                                                          ⁢                      3                                        +                                          R                      ⁢                                                                                          ⁢                      4                                                                      ⁢                Δ                            )                                                          Eqn        .                                  ⁢        6            
In equation 6, the values of resistors R31 and R32 are assumed to be equal to R3. The value of resistor R42 is equal to R4. The adjustable resistor R41 has an initial value R4 which is trimmed to cancel offset. The above equation assumes that the resistor R41 is trimmed by a percentage of its value Δ, and that Δ is much less than 1. VOS3 is the offset voltage of the third op-amp OP3. By dividing the above equations, a common amplification Acom2 and a differential amplification A2 of the second amplifier 104 can be determined to be:
                              Acom          ⁢                                          ⁢          2                =                                            R              ⁢                                                          ⁢              4                                                      R                ⁢                                                                  ⁢                3                            +                              R                ⁢                                                                  ⁢                4                                              ⁢          Δ                                    Eqn        .                                  ⁢        7                                          A          ⁢                                          ⁢          2                =                              R            ⁢                                                  ⁢            4                                R            ⁢                                                  ⁢            3                                              Eqn        .                                  ⁢        8            
From the above equations, the overall output of the instrumentation amplifier 100 may be determined by equation 9 below:VOUT≈Vin·A1·A2+(VOS1+VOS2)A1·A2+VOS3(1+A2)+Vcom·Acom2   Eqn. 9
The output depends on an amplification of the signal (e.g., Vin*A1*A2) as well as offset error terms dependent on VOS1, VOS2, and VOS3. The second and third terms of equation 9 (e.g., the offset error terms) may offset by adjusting the trimming percentage Δ to cancel the offset error in the output. However, in order to adjust the trimming percentage, the input common mode voltage Vcom must be set to a known predetermined value.
FIG. 2 shows a prior art adjustable resistor 200. The adjustable resistor 200 may, in some embodiments, be used as the adjustable resistor R41 of FIG. 1. The adjustable resistor 200 may include input node IN, output node OUT, a number of resistors R1-R10 (here labeled with their resistance values, e.g., 200 k, 300 k etc.), and switches SW0-SW7. Although specific values are shown for the resistors, it is to be understood that the adjustable resistor 200 may be configured with many different values of resistor R1-R10. Similarly, the adjustable resistor 200 may have more or less switches than the eight switches SW0-SW7 shown.
The switches SW0-SW7 may be sequentially activated by a counter (not shown) to decrease the resistance of the adjustable resistor 200. In the example adjustable resistor 200 shown, the adjustable resistor 200 has a default resistance of 500 k due to the values of R1 and R2 (e.g., 200 k and 300 k) in series between the input and output nodes (IN and OUT respectively). As the switches SW0 to SW7 are activated in sequence, the value of the adjustable resistor 200 may decrease in eight stages from −3% to −24%. Although the example adjustable resistor 200 shows only a decrease in resistance from a default value, additional resistors and switches may be added in series between the input node IN and output node OUT to allow for an increase in the resistance of adjustable resistor 200.
The adjustable resistor 200 may be optimized for a specific application. For example, when used to trim an instrumentation amplifier (e.g., amplifier 100 of FIG. 1), the step width (e.g., the number of steps between the maximum and minimum resistance) as well as the values of the maximum and minimum resistance may be optimized. The adjustable resistor 200 may be operated by a counter, which may be responsive to an output of the amplifier 100 in order to automatically determine the amount of trim needed to cancel the offset error of the amplifier 100.
FIG. 3 shows a diagram indicative of operating characteristics for an instrumentation amplifier. FIG. 3 includes graph 300, which illustrates the operating characteristics of an instrumentation amplifier such as the instrumentation amplifier 100 of FIG. 1 for two different gain configurations of the instrumentation amplifier. The x-axis of the graph 300 is the output voltage of the amplifier Vout. The y-axis of the graph 300 is the common voltage between the differential inputs Vcom. The graph 300 illustrates an example scenario wherein the amplifier 100 of FIG. 1 is configured to provide a high gain, in this case a gain of 100. The dotted lines show a scenario where an overall gain of 100 is achieved by setting the gains (e.g., by selecting resistor values) of the first amplifier 102 and the second amplifier 104 to 10. The solid lines show a scenario where the overall gain of 100 is achieved by setting a gain of the first amplifier 102 to 100 and the gain of the second amplifier 104 to 1.
Instrumentation amplifiers (e.g., amplifier 100) may be used to test a variety of circuit components. If a known current is used, the instrumentation amplifier may measure a voltage in order to determine a resistance of a circuit component, in order, for example, to check for manufacturing defects and/or damage to the component. The amplifier may need to have a sensitivity to small changes in resistance. While increasing a gain of the amplifier may increase small changes in the signal, it may also prevent easy cancellation of the offset and narrow a range of common voltages in which the instrumentation amplifier can stably operate. There remains a need for high-gain instrumentation amplifiers which can correctly cancel offset and stably operate while keeping the range of the input common mode voltage wide.